Using different modifications of a new variational approach, statical
groundstate properties of the one-band Hubbard model such as energy
and staggered magnetisation are calculated. By taking into account
additional fluctuations, the method ist gradually improved so that a
very good description of the energy in one and two dimensions can be
achieved. After a detailed discussion of the application in one dimension, extensions for two dimensions are introduced. By use of a modified
version of the variational ansatz in particular a description of the
quantum phase transition for the magnetisation should be possible.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems